Taiwan’s president-elect received jubilant approval at home and a cautious response in China a day after her sweeping victory. Taiwanese mainstream media called the election a mass win for a once struggling opposition party that historically dislikes Beijing. Officials in China are expected to wait and watch for now.

The landslide election of Tsai Ing-wen over her rival from today’s ruling party in Taiwan met a cool but calm response from Beijing. China has claimed sovereignty over the island since the 1940s and Tsai heads a political party that is backed by voters hoping for formal independence as an extension of today’s self-rule. China insists the two someday will unify.

Alexander Huang, strategic studies professor at Tamkang University in Taiwan, says China will monitor the president-elect until she takes office in May.

He says he thinks they have already, at hand, many measures to react to the changes in Taiwan, but he thinks they will give the benefit of doubt, or a "grace period." He says more people in his circle believe the "wait and see" period will be now, not after the inauguration.

Taiwanese mainstream media reacted after Tsai’s election eve comment that she wanted to work with Beijing if the island is treated equally and with dignity. Tsai is the first female president in Taiwan or China, winning 56 percent of the vote.

Media and pundits in Taiwan have focused since Saturday on what Tsai would do with China. The 59-year-old party chairperson is considered knowledgeable because she led Taiwan’s China policymaking body for three years during her party’s only term in office. People close to the president-elect, who’s a lawyer by training with a doctoral degree, also call her a skilled negotiator.

Analysts expect Tsai will figure out China, but not be cowed by it. One Taiwan newspaper said China had gone into "stop-watch-listen mode."

A woman looks at souvenir plates bearing images of Chinese President Xi Jinping, left, and late Chinese leader Mao Zedong on display for sale at a shop near Tiananmen Square in Beijing, Jan. 17, 2016.

“Tsai Ing-wen has a lot of experience dealing with China issues. Voters and other stakeholders are assuming that she will be able to manage the relationship in a way that China will react not negatively, but again we should always prepare for the worst,” says Feingold.

When Tsai’s party ruled from 2000 to 2008, its president angered China by pushing for constitutional independence. The party still draws support from pro-independence voters.

A supporter of Democratic Progressive Party (DPP) Chairperson and presidential candidate Tsai Ing-wen celebrates to preliminary results at their party headquarters in Taipei, Taiwan, Jan. 16, 2016.

During the past eight years, Taiwan’s Nationalist Party government has negotiated a series of economic deals with China, but Tsai disputes China’s precondition that both sides talk as parts of a single China, just subject to different interpretations. The Nationalist government has agreed with that precondition.

The president-elect said throughout her campaign she would avoid upsetting China and not try to break away legally. The Global Times newspaper said Sunday that Tsai’s election was neither a vote for Taiwan independence nor a gauge of relations between the two sides. Beijing's China Daily paper said Tsai should waste no time showing she's sincere about peace and stability with Beijing.

WATCH: William Ide's video report from Taipei

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